Abstract:
The method of isomonodromicJdeformations is used to investigate the asymptotic properties of solutions of the second Painlevé equation (I). The leading terms as x→±∞ of the second Painlevé functions are constructed for the general case. The parameters of the
asymptotic behavior are expressed in terms of first inteErals of the Painlevé equation, which are the monodromy data of the associated system (2) of linear ordinary differential equations with rational coefficients. The asymptotic behaviors of the real and imaginary
second Painlevé functions are separated.
Citation:
A. A. Kapaev, “Asymptotic expressions for the second Painlevй functions”, TMF, 77:3 (1988), 323–332; Theoret. and Math. Phys., 77:3 (1988), 1227–1234
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\by A.~A.~Kapaev
\paper Asymptotic expressions for the second Painlevй functions
\jour TMF
\yr 1988
\vol 77
\issue 3
\pages 323--332
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=982412}
\zmath{https://zbmath.org/?q=an:0692.34061}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 3
\pages 1227--1234
\crossref{https://doi.org/10.1007/BF01016976}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988AK72200001}
Linking options:
https://www.mathnet.ru/eng/tmf6023
https://www.mathnet.ru/eng/tmf/v77/i3/p323
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Peter D. Miller, “On the Increasing Tritronquée Solutions of the Painlevé-II Equation”, SIGMA, 14 (2018), 125, 38 pp.
L. A. Kalyakin, “Painleve II equation as a model of a resonant interaction of oscillators”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 124–135
Clarkson P.A., “Painlevé Equations - Nonlinear Special Functions”, Orthogonal Polynomials and Special Functions: Computation and Applications, Lecture Notes in Mathematics, 1883, 2006, 331–411
A. V. Kashevarov, “The second Painlevé equation in the electrostatic probe theory: Numerical solutions for the partial absorption of charged particles by the surface”, Tech. Phys., 49:1 (2004), 1
S. A. Stepin, “On Jost-Type Solutions to Quasilinear Equations with Power Nonlinearity”, Proc. Steklov Inst. Math., 236 (2002), 319–324
V. R. Kudashev, B. I. Suleimanov, “Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation”, Theoret. and Math. Phys., 118:3 (1999), 325–332
A. V. Kashevarov, “The second Painlevé equation in the electrostatic-probe theory: Numerical solutions”, Comput. Math. Math. Phys., 38:6 (1998), 950–958
V. L. Vereshchagin, “Global asymptotic formulae for the fourth Painleve transcendent”, Sb. Math., 188:12 (1997), 1739–1760
P. A. Deift, X. Zhou, “Asymptotics for the painlevé II equation”, Comm Pure Appl Math, 48:3 (1995), 277
A. V. Kitaev, “Elliptic asymptotics of the first and the second Painlevé transcendents”, Russian Math. Surveys, 49:1 (1994), 81–150
Andrei Kapaev, “Global asymptotics of the second Painlevé transcendent”, Physics Letters A, 167:4 (1992), 356
A. V. Kitaev, NATO ASI Series, 278, Painlevé Transcendents, 1992, 81
P. A. Clarkson, J. B. McLeod, NATO ASI Series, 278, Painlevé Transcendents, 1992, 1
A. R. Its, NATO ASI Series, 278, Painlevé Transcendents, 1992, 49
Martin D. Kruskal, Peter A. Clarkson, “The Painlevé‐Kowalevski and Poly‐Painlevé Tests for Integrability”, Stud Appl Math, 86:2 (1992), 87
B. I. Suleimanov, “The second Painlevé equation at a problem about nonlinear effects near caustics”, J. Math. Sci., 73:4 (1995), 482–493
A. A. Kapaev, A. V. Kitaev, “The limit transition P2→P1”, J. Math. Sci., 73:4 (1995), 460–467
A. V. Kitaev, “On symmetrical solutions for the first and second Painlevé equations”, J. Math. Sci., 73:4 (1995), 494–499
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